morality isn’t a matter of logic “all the way down,” because it has to start with some axioms,

Eliezer knows that.

From a comment on Massimo's blog...

daedalus writes:

Yudkowsky uses "logic all the way down" to mean, not bricks to construct a moral home, but formal rules to specify a moral essence. Much like how the formal rules of second order logic pin down a unique essence of the phrase "natural numbers"

Massimo writes:

Yes, and that captures the difference. Unlike numbers, morality doesn’t have “essence,” it’s a contingent concept that applies to contingent beings. That’s why morality can’t be a question of logic all the way down, unlike math.

I don't think Eliezer would agree with this, however, so it looks like there is a real difference of opinion between them. See Qiaochu_Yuan's comment for the perfect reply.